Plot hole: As the gun-toting Norseman approaches the buildings, Garry smashes the single-pane window with his handgun. It is inconceivable that the glazing in a structure near the South Pole would be single-pane glass, that would provide minimal insulation and which could be broken so easily.
Plot hole: Why doesn't Reliant know that Khan is exiled here? The Federation is so terrified and opposed to genetic engineering that it's still illegal 300 years after Khan. So why is there no warning along with the data on the Ceti Alpha system? Kirk logged what happened with Khan and his solution of marooning him. Starships use nav data to navigate star systems. Ceti Alpha 6 exploded, yet the helmsman or computer never noticed that there is one less planet than there was when Kirk was there? There is no debris from the explosion? Ceti Alpha 5 is the exact same size and was conveniently blown into the exact same orbit as Ceti Alpha 6 used to have? So there is nothing whatsoever to make the crew even suspect that it's not 6? Enterprise would have to have scanned the planets in the system to know that one was habitable for Khan. Did Ceti Alpha 6's destruction somehow magically turn Ceti Alpha 5 into its exact duplicate? If Starfleet ships have been there to map after Ceti Alpha 6 exploded, none of them bothered to check on the exiles? Pretty callous for Starfleet, don't you think? With the technology and amounts of information available to Starfleet vessels, there is NO logical reason for the Reliant to think that this planet is Ceti Alpha 6. Finally, would the Federation be willing to test a device whose exact effects will be unknown on a planet so close to another inhabited one? (00:21:00)
Suggested correction: The answer is yes: against all known laws of science, the inexplicable explosion of Ceti Alpha VI led to Ceti Alpha V conveniently taking its orbit and making it easy to mistake for its former sister planet. A mistake would've been to give an explanation that can be debunked. By leaving it to "somehow" the movie leaves it open to a million possible rationalizations. You can even make a whole other story about the crazy circumstances that led to this incredible result.
Plot hole: In what appears to be at least an hour or so after curfew is put in effect, Challis goes to a liquor store. Even if he didn't know about the curfew, why would the liquor store still be open?
